How would I go about turning this object into a 3D model with the same colours?
It's not easy to turn a 2d image into a 3d object.  What I would recommend is to create a "turnaround" as a first step.  Basically this involves sketching a front, side, top, and/or back view of the character.  An example is here.  

This is very important to figure out the shapes of the model from multiple angles. 

Once you have the turnaround, you can import it as Background Images in blender and assign it to the front and side views to use as a guide.  From there model on top of the images.  There are many tutorials for that kind of modeling, like the famous Joan of Arc Tutorial.

Good luck!  The turnaround sheet is likely the hardest part.